The main error in your frame to support a fatigue machine is that you have not applied the principles of rigid structures to the frame.
Look at the first mode at 20Hz, do you see those S bends? You get rid of that by taking a rectangle of plywood and screwing it down to the legs on the each end. You already have a narrow panel on the ends at the top. That will be replaced with the larger panel that covers the whole end face. You will want a beam at each end at the top to complete the frame of the tabletop.
Look at the second mode, the S bends in the other plane are removed by taking a larger plywood panel and screwing it to the legs on the front and back of the frame.
Finally, look at Mode 5, the tabletop of the frame needs a rectangular sheet of plywood screwed down to the four edges.
Those 5 sheets of plywood are called shear panels. If the four feet are screwed to the ground, then you have a rigid structure.
If the four feet are not screwed to the ground, then you need a sixth plywood panel for the bottom, but move the four beams that are below the middle of the vertical beams and move them all the way to the floor so you have those four beams to screw the bottom panel onto. Now you will have a six-sided box screwed down to 12 beams at each of the 12 edges and that is a rigid structure.
The tabletop may need to be thicker to support the mounting of the fatigue machine, but instead of thin steel strips, lay down two wooden beams like the legs across the full width to get rid of the bending in the thin strips seen in mode 2. This is in addition to the thin plywood tabletop shear panel.
After you have done that, then we can talk about moving from an isotropic to an orthotropic material model for wood.
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